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Math Help - geometric kite problem

  1. #1
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    geometric kite problem

    ABCD is a kite. Squares have been constructed on each of the four sides of this kite acting as a base. The centroid of each square has been determined and a quadrilateral has been constructed with these centre points as vertices.

    I would like to show whether it is a trapezium or not. I think it is but i can not manage to get the proof. if anyone is interested please let me know and i'll email you the image generated by cabri for this problem. My email is gauci_mariella@hotmail.com
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  2. #2
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    Quote Originally Posted by marzi View Post
    ABCD is a kite. Squares have been constructed on each of the four sides of this kite acting as a base. The centroid of each square has been determined and a quadrilateral has been constructed with these centre points as vertices.

    I would like to show whether it is a trapezium or not. I think it is but i can not manage to get the proof. ...
    You are dealing with a symmetric kite. The axis of symmetry is the line (BD).

    You add congruent figures smmetrical to the existing axis. Therefore corresponding points of the squares (You can take the vertices or the center, or midpoints of sides,...) are connected by lines perpendicular to the axis of symmetry. That means these connections are parallels. Thus the new figur is a trapezium.

    If you want to proof that this trapezium is symmetric too, then show that the lines which don't intersect the axis (blue lines) are symmetric to each other.
    Attached Thumbnails Attached Thumbnails geometric kite problem-symdrach_ergaenz.gif  
    Last edited by earboth; February 16th 2008 at 06:27 AM.
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